Finite Group Databasebeta

← #13079920

Subgroups — #13079920

Order 1408.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623174C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4#10622656C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic
6#10622504C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622468C211yesmaximal, characteristic, complemented
10#10622413C211yesmaximal, characteristic, complemented
11#10622412C211yesmaximal, characteristic, complemented
12#10622408C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622348C211yesmaximal, characteristic
15#10622333C211yesmaximal, characteristic, complemented
16C11×C22⋊Q8C2211yescharacteristic
17C11×#117C2211yescharacteristic
18#67000C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20#66983C2211yescharacteristic
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23#66951—21no—
24#66950—21no—
25#66946C2211yescharacteristic
26#66943C2211yescharacteristic
27#66943C2211yescharacteristic
28#66941C2211yescharacteristic
29#66941C2211yescharacteristic
30#66941C2211yescharacteristic
31#66938—21no—
32#66936—21no—
33#66931—21no—
34#66931—21no—
35#66923—21no—
36#66922—21no—
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#103C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66881C2211yescharacteristic
48#66881C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C22⋊Dic11D411yescharacteristic
78C22⋊Dic11D411yescharacteristic
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11D411yescharacteristic
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3244—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104C22×D11—21no—
105Q8×C11—21no—
106Q8×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2411yescharacteristic
115C22⋊D11—81no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—81no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124D44—21no—
125D44—21no—
126C4×D11—81no—
127Dic22—81no—
128Dic22—81no—
129Dic22—81no—
130C8×C11—21no—
131C8×C11—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134#544—111no—
135#542—111no—
136#501—111no—
137#498—111no—
138#489—111no—
139#488—111no—
140#485D1111yescharacteristic, complemented
141#483—111no—
142#482—111no—
143#481—111no—
144#479—111no—
145#478—111no—
146#476—111no—
147#475—111no—
148#433—111no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11C22×D411yescharacteristic
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C112−1+411yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—21no—
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—111no—
173C4⋊Q8—221no—
174#126—221no—
175#125—111no—
176#125—111no—
177#125—221no—
178#124—111no—
179#124—221no—
180#123—221no—
181C22⋊Q8—221no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8C2×D1111yescharacteristic
185#121—111no—
186C4×Q8—111no—
187C4×D4—111no—
188#117—111no—
189#117C2×D1111yescharacteristic
190C2×C4⋊C4—111no—
191#107—111no—
192#107C2×D1111yescharacteristic
193#106—111no—
194#106—111no—
195#106—111no—
196#106—111no—
197#106—111no—
198#106C2×D1111yescharacteristic
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103C2×D1111yescharacteristic
204#103C2×D1111yescharacteristic
205#102—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209C22⋊C8—111no—
210C22⋊C8C2×D1111yescharacteristic
211#97—111no—
212C4×C8—111no—
213C2×C11—41no—
214C2×C11#53611yescharacteristic
215C2×C11#57711yescharacteristic
216C2×C11#57711yescharacteristic
217D11—81no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C2×D4—221no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4C22×D1111yescharacteristic
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—111no—
252C22⋊C4—111no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C42—21no—
258C42—111no—
259C42—111no—
260C42—221no—
261C11#324411yescharacteristic, complemented, Sylow
262C23—221no—
263C23D4×D1111yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—881no—
267Q8—881no—
268Q8—881no—
269D4—221no—
270D4—221no—
271D4—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4D4×D1111yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—221no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704311yescharacteristic
313C4#6704311yescharacteristic
314C2—41no—
315C2—881no—
316C2#1062317911yescharacteristic
317C2#1062330111yescharacteristic
318C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#485D11
hypocenterC11#3244
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10623050C2semidirect
3. C11×#485C2semidirect
4. #10622656C2semidirect
6. #10622504C2semidirect
7. #10622489C2semidirect
8. #10622483C2semidirect
9. #10622468C2semidirect
10. #10622413C2semidirect
11. #10622412C2semidirect
12. #10622408C2semidirect
13. #10622404C2semidirect
15. #10622333C2semidirect
140. #485D11semidirect
261. C11#3244semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106231742
#106230502
C11×#4852
#106226562
#106226162
#106225042
#106224892
#106224832
#106224682
#106224132
#106224122
#106224082
#106224042
#106223482
#106223332
#324411